{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:XRZDCPKKKOC2FNXU7T6XY2G2C5","short_pith_number":"pith:XRZDCPKK","canonical_record":{"source":{"id":"1907.02769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-05T11:02:39Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"ab88af2288fb4ee9c13771d8b9af90a9c26f2539fdd69ce0d32553fd62912122","abstract_canon_sha256":"ca0a9cb1f011421bf6bd75c2f854f4d16f38dbe481d1663e8425ff769f944ec7"},"schema_version":"1.0"},"canonical_sha256":"bc72313d4a5385a2b6f4fcfd7c68da17497a47405399700b071e21cdb4e2f2cf","source":{"kind":"arxiv","id":"1907.02769","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02769","created_at":"2026-05-17T23:41:23Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02769v1","created_at":"2026-05-17T23:41:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02769","created_at":"2026-05-17T23:41:23Z"},{"alias_kind":"pith_short_12","alias_value":"XRZDCPKKKOC2","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XRZDCPKKKOC2FNXU","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XRZDCPKK","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:XRZDCPKKKOC2FNXU7T6XY2G2C5","target":"record","payload":{"canonical_record":{"source":{"id":"1907.02769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-05T11:02:39Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"ab88af2288fb4ee9c13771d8b9af90a9c26f2539fdd69ce0d32553fd62912122","abstract_canon_sha256":"ca0a9cb1f011421bf6bd75c2f854f4d16f38dbe481d1663e8425ff769f944ec7"},"schema_version":"1.0"},"canonical_sha256":"bc72313d4a5385a2b6f4fcfd7c68da17497a47405399700b071e21cdb4e2f2cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:23.197677Z","signature_b64":"6dYmWxlooCxzJjWJtzex6065sSV7EEXO8Ti0bq+qVR7SaOrhJtZXe2PDAhQX9qngvK8KyQuFRwbYc53yiJF+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc72313d4a5385a2b6f4fcfd7c68da17497a47405399700b071e21cdb4e2f2cf","last_reissued_at":"2026-05-17T23:41:23.197001Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:23.197001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.02769","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SFXWwKO5UHSFv1hiAITnfAhZZVJuzxIWCc0Augfsc/ScEJ7fq/pUxBwsj/89muW3n/W6VxSOJqiNR6lR9ey+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:21:31.625892Z"},"content_sha256":"959b4fe8c5eef9744051003d3ce527d2876805a0090babc071fb77a4d083a270","schema_version":"1.0","event_id":"sha256:959b4fe8c5eef9744051003d3ce527d2876805a0090babc071fb77a4d083a270"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:XRZDCPKKKOC2FNXU7T6XY2G2C5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A comparison of various analytic choice principles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"math.LO","authors_text":"Paul-Elliot Angl\\`es d'Auriac, Takayuki Kihara","submitted_at":"2019-07-05T11:02:39Z","abstract_excerpt":"We investigate computability theoretic and descriptive set theoretic contents of various kinds of analytic choice principles by performing detailed analysis of the Medvedev lattice of $\\Sigma^1_1$-closed sets. Among others, we solve an open problem on the Weihrauch degree of the parallelization of the $\\Sigma^1_1$-choice principle on the integers. Harrington's unpublished result on a jump hierarchy along a pseudo-well-ordering plays a key role in solving the problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02769","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eHkTr0v7qW2c8WeLn0tWedrUy+F7PzCxNEhHe9W3jG4F6oUb4lXv+cC43v7qlWxP/t8ylN3S1LxiiL5ylipxCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:21:31.626569Z"},"content_sha256":"be8706d62c5481b6e0d001e389bae407ba05c5806954223b64f9d9de5b8ebb07","schema_version":"1.0","event_id":"sha256:be8706d62c5481b6e0d001e389bae407ba05c5806954223b64f9d9de5b8ebb07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XRZDCPKKKOC2FNXU7T6XY2G2C5/bundle.json","state_url":"https://pith.science/pith/XRZDCPKKKOC2FNXU7T6XY2G2C5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XRZDCPKKKOC2FNXU7T6XY2G2C5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T18:21:31Z","links":{"resolver":"https://pith.science/pith/XRZDCPKKKOC2FNXU7T6XY2G2C5","bundle":"https://pith.science/pith/XRZDCPKKKOC2FNXU7T6XY2G2C5/bundle.json","state":"https://pith.science/pith/XRZDCPKKKOC2FNXU7T6XY2G2C5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XRZDCPKKKOC2FNXU7T6XY2G2C5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XRZDCPKKKOC2FNXU7T6XY2G2C5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ca0a9cb1f011421bf6bd75c2f854f4d16f38dbe481d1663e8425ff769f944ec7","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-05T11:02:39Z","title_canon_sha256":"ab88af2288fb4ee9c13771d8b9af90a9c26f2539fdd69ce0d32553fd62912122"},"schema_version":"1.0","source":{"id":"1907.02769","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02769","created_at":"2026-05-17T23:41:23Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02769v1","created_at":"2026-05-17T23:41:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02769","created_at":"2026-05-17T23:41:23Z"},{"alias_kind":"pith_short_12","alias_value":"XRZDCPKKKOC2","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XRZDCPKKKOC2FNXU","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XRZDCPKK","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:be8706d62c5481b6e0d001e389bae407ba05c5806954223b64f9d9de5b8ebb07","target":"graph","created_at":"2026-05-17T23:41:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We investigate computability theoretic and descriptive set theoretic contents of various kinds of analytic choice principles by performing detailed analysis of the Medvedev lattice of $\\Sigma^1_1$-closed sets. Among others, we solve an open problem on the Weihrauch degree of the parallelization of the $\\Sigma^1_1$-choice principle on the integers. Harrington's unpublished result on a jump hierarchy along a pseudo-well-ordering plays a key role in solving the problem.","authors_text":"Paul-Elliot Angl\\`es d'Auriac, Takayuki Kihara","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-05T11:02:39Z","title":"A comparison of various analytic choice principles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02769","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:959b4fe8c5eef9744051003d3ce527d2876805a0090babc071fb77a4d083a270","target":"record","created_at":"2026-05-17T23:41:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ca0a9cb1f011421bf6bd75c2f854f4d16f38dbe481d1663e8425ff769f944ec7","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-07-05T11:02:39Z","title_canon_sha256":"ab88af2288fb4ee9c13771d8b9af90a9c26f2539fdd69ce0d32553fd62912122"},"schema_version":"1.0","source":{"id":"1907.02769","kind":"arxiv","version":1}},"canonical_sha256":"bc72313d4a5385a2b6f4fcfd7c68da17497a47405399700b071e21cdb4e2f2cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc72313d4a5385a2b6f4fcfd7c68da17497a47405399700b071e21cdb4e2f2cf","first_computed_at":"2026-05-17T23:41:23.197001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:23.197001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6dYmWxlooCxzJjWJtzex6065sSV7EEXO8Ti0bq+qVR7SaOrhJtZXe2PDAhQX9qngvK8KyQuFRwbYc53yiJF+AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:23.197677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.02769","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:959b4fe8c5eef9744051003d3ce527d2876805a0090babc071fb77a4d083a270","sha256:be8706d62c5481b6e0d001e389bae407ba05c5806954223b64f9d9de5b8ebb07"],"state_sha256":"844f41d3a5bb2ed7ca22fb48fff66061ecac1a3f4c50e19eabfa03b929bdcc1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V2T5WnW5BGjN2g3EFnZmi8H9WmJgpLIVUGrh5e0N2bsABnvlMt+rhClEYN9QqY0BkfoOpYWMKTG6XXMvx1JoBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:21:31.630257Z","bundle_sha256":"49a7e90ed98c2a89a24de853efebbba2bf7662701dc1f095d4f25549be31634f"}}